For some reason, all of your source data is being treated as text. If source data is properly recognised as numeric, the text qualifier will not be applied to it.
To check this, when you are running the wizard, click on the 'Edit Transform' button on the Configure Flat File Destination dialog. That will take you into a screen where you can view and, if necessary, amend the datatypes of the fields which you are exporting.
I am assuming that this is just a one-off export? If not, you may need to edit the package created by the wizard in BIDS to get it refined and working exactly as you want it.
Phil